# Two particles have equal kenetic energies

1. Feb 9, 2004

### napier212121

if two particles have equal kenetic energies, do they have the same momentum?

2. Feb 9, 2004

### lpfan4yrs04

NO! Just because something has the same kinetic energy doesn't mean it has the same momentum. There are a number of factors that could affect it.

3. Feb 9, 2004

### HallsofIvy

Staff Emeritus
Kinetic energy of an object with mass m and velocity v is (1/2)mv2. Momentum is mv.

Take for example, an object with mass 4kg and speed 1 m/s. Its kinetic energy is (1/2)(4)(1)2= 2 Joules and its momentum is (4)(1)= 4 kgm/s. Take a second object with mass 1kg and speed 2 m/s. It has kinetic energy (1/2)(1)(2)2= 2 Joules also but its momentum is (1)(2)= 2 kgm/s.

Last edited by a moderator: Feb 9, 2004
4. Feb 9, 2004

### GRQC

Well, kinetic energy (for particles, as the question originally asked) is probably more likely to be $K = (\gamma - 1) mc^2$, i.e. relativistic kinetic energy, which reduces to the Newtonian expression in the limit of small v.